I have some response data from an experiment which uses appraisal methods to assign scores based on various attributes. The scores are awarded (in part) from visual observations of biological condition, i.e. the scales are ordinal, and also from quantitative measurements. The results of the visual observations and the mensuration are combined and the final response data is continuous. I have four different appraisal methods which all work in this way, using slightly different criteria and scoring.
The null hypothesis which I am testing is that my treatment has no effect on the score. When I run an ANOVA or linear model and examine the residuals, some are returned as normally distributed and some are not. I intend to publish the paper.
How do I deal with this in my analysis? Is it acceptable to run two types of test (ANOVA and a non-parametric test). I am using R (v 3.4.4) for my analyses.
Here is an example of one response using one way ANOVA.
The SW test shows non-normal residuals
Shapiro-Wilk normality test data: residuals(aov_BURNLEY) W = 0.8724, p-value = 8.776e-08
Another example using one way ANOVA.
The SW test shows normally distributed residuals
Shapiro-Wilk normality test data: residuals(aov_CTLA) W = 0.98722, p-value = 0.4526
And another example using one way ANOVA.
The SW test shows non-normally distributed residuals
Shapiro-Wilk normality test data: residuals(aov_STEM) W = 0.37409, p-value < 2.2e-16